You simply do not need to believe this. The universe doesn't need to be "stored" somewhere.

> Quantum Computing is firmly based on pretending that this isn't how it is, that somehow you can squeeze 2^n bits of information out of a system with 'n' parts to it.

Quantum computing does not believe this. It is a theorem that you can only get n bits out of n qubits, and quantum computing speedups do not rely otherwise.

Noise is hard, but error correction is a mathematically sound response.

It won't be factoring large numbers yet because that computation requires the ability to perform millions of operations on thousands of qubits without any errors. You need very good error correction to do that, but luckily that's the other thing they demonstrated. Only when they do error correction, they are basically combining their system down into one effective qubit. They'll need to scale by several orders of magnitude to have hundreds of error corrected qubits to do factoring.

1) What you've written, where H is independent of t is reducible to just the Eigenvalue problem for H. Certainly better understood than fluid dynamics. Even with time-dependent hamiltonians we have decent tools for talking about the solutions (Dyson series).

2) Of course for certain values of H, (esp. in continuous space) you can contrive ways of making the eigenvalue problem hard, but you don't have to go as far as quantum mechanics to find difficulty. Just take three bodies under newton's gravitation.

Yes, the quantum n-body problem is exponentially harder in n, but that's a fundamentally different type of "hardness" than the hardness of Navier-Stokes.

The representation of the quantum state as a bar chart is difficult to interpret and provides little intuition. The fact is, visualizing vectors in high-dimensional spaces is hard, much less vectors in high-dimensional complex spaces. Bra-ket notation is pretty much the best thing we have right now.

But more generally, "Quantum programming" will almost certainly look nothing like this. This is like programming a classical computer by describing a boolean circuit. It's an extremely useful model for researchers working with actual hardware, but there's a reason we currently program with lambda calculi, not NAND gates. Understanding how to capture the possibilities of quantum circuits in a higher-level language is an open problem. Many interesting attempts have been made at solving it, but none convincingly in my opinion.

  for word, count in Counter(open('test.txt').read().lower().split()).most_common():
      print word, count

Yes, that is the point of welfare. Universal income is a type of welfare. It is a form of welfare which is preferable to other forms because of its simplicity of implementation.

So, if the question you want to ask is "what is some property of the solution of the (sparse) set of linear equations" rather than wanting to know the (inherently O(n)) solution itself, you can get exponential speedup.